Data Analysis with Microsoft Excel: Updated for Office 2007

422 Statistical Methods

Interpreting the Analysis of Variance Table

The Analysis of Variance table appears as in Figure 10-22, with the columns

resized to show the labels (you might have to scroll to see this part of the

output).

There are three effects now, whereas the one-way analysis had just one.

The three effects are Sample for the type effect (row 25), Columns for the

cola effect (row 26), and Interaction for the interaction between type and

cola (row 27). The Within row (row 28) displays the within sum of squares,

also known as the error sum of squares.

As we saw earlier with the one-way ANOVA, the two-way ANOVA breaks

the total sum of squares into different parts. If we designate SST as the

sum of squares for the cola type, SSC as the sum of squares for cola brand,

SSI for the interaction between brand and type, and SSE for random

error, then

Total 5 SST 1 SSC 1 SSI 1 SSE

In this data set, the values for the various sums of squares are

SST 1,880.00

SSC 183,750.50

SSI 4,903.38

SSE 73,572.58

The degrees of freedom for each factor are equal to the number of levels

in the factor minus 1. There are two cola types, diet and regular, so the de-

grees of freedom are 1. There are 3 degrees of freedom in the four cola brands

(Coke, Pepsi, Shasta, and generic). The degrees of freedom for the interaction

term are equal to the product of the degrees of freedom for the two factors. In

this case, that would be 1 3353. Finally, there are n 21 , or 47, degrees of

freedom for the total sum of squares, leaving 47 211131325 40 degrees

of freedom for the error sum of squares. Note that the total degrees of freedom

are equal to the sum of the degrees of freedom for each term in the model. In

other words, if DFT are the degrees of freedom for the cola type, DFC are the

Figure 10-22

Two-way

ANOVA table

error term

type effect (diet or

regular)

cola effect (cola, pepsi,

shasta, or generic)

interaction of the type
and cola effect